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A COMPREHENSIVE METHOD FOR DIAGNOSING PLANNING IN PRIMARY
SCHOOL
A.Z. Zak, Leading Researcher
Psychological Institute of Russian Academy of Education (Russia, Moscow)
DOLW.24412/2500-1000-2021-6-2-32-39
Abstract. The study developed a complex of two tasks designed to determine the formation of cognitive metasubject competence associated with the ability to plan in primary schoolchildren, in particular, in second-graders. The problems of the first task create more complex conditions for planning the solution than the problems of the second task. This approach makes it possible to distinguish in the classroom not two, as usual, but three groups of children according to the formation of cognitive actions. The first group consists of children who solved the problems of both tasks, the second group - children who solved the problems of only the second task, the third group - children who did not solve the problems of both tasks. The testing of the complex showed its effectiveness for a more complete than usual diagnosis of the ability to plan the solution of problems in primary grades.
Keywords: the ability to plan, second graders, a set of two tasks, the "Letters, numbers" technique, the "Postman" technique.
1. Introduction
According to the provisions of the new Federal State Educational Standard of primary general education [1], the mastering of the basic educational program by children in the elementary grades of school should lead not only to the achievement of subject educational results based on the assimilation of the content of programs of specific academic disciplines.
The main idea of the new FSES is that mastering the curriculum should lead to the achievement of metasubject results, which reflect, in particular, the formation of a variety of cognitive competencies.
One of these competencies is the ability to plan the solution of problems. This skill, according to the fundamental provisions of developmental psychology, is associated with such a psychological neoplasm of primary school age as the ability to act "in the mind", in the internal plane [2].
From the provisions of the new FSES, it also follows that it is necessary to control the level of formation of the discussed metasub-ject competence, not only at the exit from primary school, but also in the learning process in primary grades. In this case, opportunities are created, already at the early stages of mastering this competence, to identify
children with insufficient formation of the ability to plan. This will allow such children to be provided with timely support and assistance.
1.1. Features of the complex diagnostic method
The present study was aimed at developing a comprehensive method for determining the formation of cognitive competence related to planning in primary schoolchildren (in particular, in second graders). The meaning of this method is to identify children with different degrees of planning formation using the material of different tasks.
At the same time, we believed that children should be offered to solve problems based on non-educational material. As noted by the well-known Russian psychologist VV Davydov, "... in psychology it is generally accepted that with the help of this material it is possible to reveal the general features of the child's mental actions, regardless of their specific subject content" [3, p.334]. In other words, this approach minimizes the influence of the degree of mastery of subject competences on the success of children's actions in solving problems.
It should be specially noted that there is significant research experience in the use of various non-educational tasks in experimental
work with younger schoolchildren in the study of various cognitive actions, in particular those actions that are associated with solving problems.
So, in Russian psychology, in the study of planning as a component of theoretical thinking associated with the analysis of problem conditions, spatial combinatorial problems are used [4]. In tasks of this type, it is necessary, on the basis of the given, initial arrangement of objects on the plane, to obtain their required arrangement. To do this, the location of objects in the original location should be changed according to certain rules for the proposed number of actions.
In another study [5], when studying planning as a component of theoretical thinking associated with reflection, labyrinth problems "with rules" are used. In tasks of this type, it is proposed to move imaginary characters between two known points on the proposed playing field for the required number of actions of a certain nature.
In foreign psychology, in the study of planning in younger schoolchildren, problems of a non-educational nature are also used. Such problems constitute a technique known as the "Tower of London" task (by T. Shallis [6]). The material of the technique includes two boards with pegs and several beads of different colors. It is required to arrange a certain number of beads on the pegs in the required number of steps. This technique was used to determine the factors of complexity of solving its problems [7]. It was shown that these factors are the hierarchy of target positions, the hierarchy of initial positions, and the number of available solutions.
The problems known as the "Tower of Hanoi" task are also used in a number of studies to study planning. The material of the problems includes three rods and a row of discs of different diameters, which can slide on any rod. At the beginning of the problem, a rod is proposed, on which discs are put on in order of decreasing size, thus approaching a conical shape (the largest disc is at the bottom, the smallest at the top). It is required to move all these disks one by one to another rod, observing the rule: no disk can be placed on top of a disk that is smaller than it.
These problems were used, in particular, in a study aimed at studying the relationship between the ability to plan and short-term memory [8]. It was shown that the failure of planning in solving the problems of the noted technique is predetermined by the low efficiency of visual-spatial short-term memory.
In another study related to the study of non-teaching planning [9], the aim was to find out to what extent the objectives of the methods "Tower of London" and "Tower of Hanoi" are interchangeable in experimental work with children. It has been shown that the "Tower of Hanoi" problems create more difficult conditions for younger students to effectively plan a successful solution than the "Tower of London" problems.
In the present study, the tasks of a non-educational nature were spatially combinatorial tasks (Letters, numbers ") and labyrinth problems with rules (" Postman "). In problems of the first type, it was required to arrange letters according to certain rules for the required number of actions in the same places on which the numbers are located. In tasks of the second type, it was required to mentally change, according to certain rules, the location of an imaginary character on the playing field.
The study was based on the assumption that the use of a complex of two tasks provides a more complete and more accurate diagnosis of the formation of this cognitive competence in second-graders than the use of a separate task. In this case, the tasks in the complex should be selected in such a way that the successful completion of one of the tasks is associated with the child's ability to carry out more complex orientation in the conditions of the proposed tasks, and the fulfillment of another task - with the ability to carry out less complex orientation.
Such an approach will make it possible to characterize the formation of this cognitive competence in a certain group of children (in particular, second-graders) with greater specificity (as opposed to diagnostics associated with the use of only one task). In this case, as can be assumed, one part of the children will cope with the problems of both tasks, the other - with the problems of only one task, the successful solution of which presupposes less
complex orientation in their conditions, the third part will not cope with the problems of both tasks.
Thus, it becomes possible to distinguish in a certain group of second-graders not only two subgroups of children, in one of whom the diagnosed competence has been formed, since the problems of the proposed task have been solved, and in the other subgroup this competence has not been formed, since the problems of the proposed task have not been solved. Conditions are created for the selection of three subgroups - in particular, it is possible to characterize the subgroup whose children successfully solved the tasks of only one task, since their solution requires less complex orientation in the conditions.
In other words, diagnostics using two tasks, differing in the complexity of their constituent tasks, makes it possible to single out children with a greater and lesser degree of formation of the assessed cognitive competence, and not only children whose competence is formed and not formed.
1.2 Types of planning
As you know, human cognitive activity can be aimed at reflecting the internal connections of objects and phenomena (theoretical, meaningful, reasonable knowledge) and at the reflection of their external connections (empirical, formal, rational knowledge), - see, in particular, [10].
Based on the characteristics of substantive and formal cognition, planning, as a type of universal cognitive action, on the basis of which the corresponding cognitive competence is formed, is characterized as follows.
Planning as an action that is realized in the inner, mental plane, most intensively, according to the provisions of developmental psychology [2], is formed precisely at primary school age, since during this period the basic skills of educational activity are formed.
Characterizing the new qualities of the psyche in children at this age, V. V. Davydov points out: "The more "steps" of his actions a child can foresee and the more carefully he can compare their different options, the more successfully he will control the actual decision tasks. The need for control and self-control in educational activities, as well as a number of its other features (for example, the
requirement for verbal reports, assessment) create favorable conditions for the formation of younger students' ability to plan and perform actions for themselves, in the internal plan "[2 , p. 83].
An internal action plan, formed at a high level, allows the child, as shown in a number of works (see, for example, [11], [12]), to more easily perform orientation in the conditions of the task, highlighting data relations in them and denoting such relations with various kinds of signs and symbols. All this provides the ability to correctly program the solution to the problem, presenting and keeping in the internal plan the possible intermediate results of the proposed actions when correlating them with the ultimate goal and with each other, comparing and evaluating different options for their implementation.
In the above studies, two levels of development of an internal action plan were distinguished, since planning as a mental action associated with building a program of steps to achieve the required result is carried out in different ways.
At the first level, a person outlines and performs each step within a certain sequence separately, programs the execution of the required sequence of actions in parts, in separate links. These links are not linked by him into a single system, since planning elements alternate with the implementation of individual steps of the solution. This is formal, partial planning.
At the second level, the whole sequence of steps is outlined by a person immediately, before the first step is completed. He, therefore, programs the execution of the required sequence of actions as a whole, in full. At the same time, different options for performing whole sequences of steps are compared and acceptable ways to achieve the goal are selected. In this case, the subsequent links of the required action are planned simultaneously with the previous ones, and the previous ones are planned taking into account the possible options for performing the subsequent ones. This is inclusive planning.
2.Materials and methods
2.1. The task "Letters, numbers"
In accordance with these concepts, a general scheme of a two-part experimental situa-
tion was developed, designed to determine the characteristics of planning. In the first part of this situation (according to Y.A. Ponomarev [12]), the subject is invited to master some simple action. In the second part, it is required to solve several problems for building the sequence of these actions.
In our study [11], it was found that the selection of problems in the second part of this situation must meet the following requirements. First, the sequence of executive actions should gradually increase from the first task to the last. Secondly, there should be at least two tasks with the same number of executive actions.
Thirdly, and most importantly, tasks should not have a common principle of solution, so that each time it is necessary to experiment mentally, re-developing an ever-increasing sequence of actions.
To determine the type of cognitive action (formal or meaningful), on the basis of which the ability to plan is formed, a complex of two tasks is used. Each task uses an experimental situation where the child is asked to solve a number of problems with a gradually
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The proposed set of tasks needs to be solved in a visual-figurative form in a group experiment. In the first series of experiments, two sessions were conducted on the material of the assignment "Letters, numbers". A total of 46 people participated in the training.
2.2. The task "Postman"
The second series of experiments was carried out on the material of the "Postman" assignment, also in two group sessions and with the same children who participated in the first series.
The "Postman" task includes a series of problems related to the mental change of the
increasing number of executive actions. In this case, the problems do not have a common solution.
One task - "Letters, numbers" - includes a series of problems related to changing the location of objects on the playing field in an imaginary plan. Moreover, the formal rules for solving these problems are such that possible changes in the location of objects are not clearly represented.
For example, the sequence of letters T T P must be changed in one action so that the same letters are located in the same way as the same numbers 8 7 7 (solution: the extreme letters T and P will be swapped). Thus, in one action, there are two interrelated changes in the locations of objects, since the letters T and P move simultaneously: the letter T in the place of the letter P, and the letter P in the place of the letter T.
In this task, the solution of the subsequent problems of the series required the execution of a larger number of executive actions (to change the location of objects) than the solution of the previous problems:
location of an imaginary character ("postman") on the playing field. In contrast to the tasks of the "Letters, numbers" task, the formal rules for solving the "Postman" problems allow visualization of possible changes in the location of the postman (ie, his expected movements).
This is due to the fact that the postman's mental movements are made in relation to the playing field, where circles ("houses where the postman brings letters") and lines ("paths along which the postman walks") are depicted - see, for example, the condition of the sample problem on playing field (fig. 1):
S N F F---------9 9 4 6 (2 actions)
J D P D J--------- 3 4 4 5 5 (2 actions)
X R L R R P--------- 8 5 8 4 6 8 (3 actions)
L T R T T P T-------6 6 6 4 5 6 7 (3 actions)
R R S P R M R N -— 9 4 2 4 8 4 6 4 (4 actions) S S V L S S N S G — 6 4 3 3 3 5 3 7 3 (4 steps)
Fig. 1. Conditions of the sample problem
Before solving such problems, children are told: "The circles are houses, two images in each circle are residents, and the lines between the circles are paths along which the postman walks and delivers letters." It is also noted that the postman observes a two-part rule when traveling. The first part, - positive,
- prescribes that you can only move along such paths that connect houses where there is the same inhabitant. The second part, - negative, - prescribes that you cannot move along those paths that connect houses where there is no identical inhabitant.
So, about the situation shown in Fig. 1, the following is said: "The postman left the house
- the post office (there live a triangle and a dot) walked along one path to some house and then along another path came to the
house where the circle and the arrow live. You need to find out which two paths the postman took: first up, then down, or first down, then up? "
When discussing this problem, some children offer the correct solution: "First the postman goes down, then he goes up," other children offer the wrong solution: "First he goes up, then down." In both cases, the experimenter asks the children to recall the postman's movement rule and use this rule to justify their answers.
The "Postman" task includes the following series of problems (where the letter and the number are "residents", and the rectangles represent the "houses" that the postman "visited"), - (Fig. 2):
Fig. 2. Problems of the task "Postman"
The proposed series of problems had to be solved in a visual-figurative form in a group experiment. At the beginning of the lesson, a
playing field was depicted on the blackboard for solving a series of problems in the "Postman" task (Fig. 3):
Fig. 3. The playing field for solving problems "Postman"
Thus, in the tasks of the "Postman" task, possible changes in the location of an imaginary object (ie, possible movements of the postman) are presented visually. In this case, there is an independent, unidirectional mental movement of one object along visible lines.
In contrast, in the tasks of the "Letters, numbers" task, possible changes to objects are not clearly presented. In this case, there is an interdependent, multidirectional mental movement of two objects (movement of two letters) and there is no support for visible landmarks.
3.Results
In each task of the complex under consideration ("Letters, numbers" and "Postman"), the solution of subsequent problems required a larger number of executive actions (to change the location of objects) than the solution of the previous.
On this basis, when processing the results of solving problems and assessing the formation of planning, we relied on the following provisions common to both tasks.
If the child was able to correctly solve only one (first) problem in any task or could not solve any problem, then it was assumed that in these cases there was no planning. As shown by observations in individual experiments, these children acted at random, in a random way, without any preliminary orientation in the problem. This indicated a random
solution to the problem that had nothing to do with planning.
If the child was able to correctly solve only the first two problems (in two actions) and did not cope with the rest of the problems, then it was assumed that he carried out partial planning in solving problems. In individual experiments, it was seen how these children first studied the conditions of the problem, then outlined and performed the first action. Then the conditions of the problem were considered again, the second action was outlined and carried out. Thus, the discussed group of children carried out the solution of problems on the basis of formal, partial planning.
If the child was able to correctly solve problems in two and three actions or problems in two, three and four actions, then it was assumed that he solved the problems on the basis of meaningful, holistic planning. Observations in individual experiments indicate that these children, after studying the conditions of the problem, first planned all the necessary actions, made a complete plan for the solution, and then carried out all the planned actions.
The results of processing the results of solving tasks by children of the tasks "Letters, numbers" and "Postman" are presented in the table.
Table. The number of children who solved problems on the basis of random actions, formal and meaningful planning (in %)
Tasks Types of problem solving
Based random action Based on formal planning Based on meaningful planning
"Letters, numbers" 13,1 65,2 21,7*
"Postman" 4,3 52,2 43,5*
Note: * p <0.05.
The processing of the obtained results showed that meaningful planning in solving the problems of the task "Letters, numbers" was able to carry out 21.7% of the subjects, and when solving the problems of the task "Postman" - 43.5%, - the noted indicators are statistically significant (at p <0.05).
The noted data allow us to conclude that, indeed, as expected, the solution of the problems of the "Letters, numbers" task is more difficult to plan than the solution of the problems of the "Postman" task. This is due, as noted, to the fact that in the problems of the "Letters, numbers" task, possible changes in the location of objects are not clearly represented, and in the problems of the "Postman" task, possible changes in the location of objects (that is, the movement of an imaginary character when relying on actually presented lines) can be correlated with the corresponding images.
4. Conclusion
Analysis of the data obtained as a result of solving the problems of the tasks "Letters, numbers" and "Postman" by children, allows us to note that a more complete characteristic of planning is associated with the selection of children with different degrees of formation of this competence. To do this, children should be encouraged to solve problems with different rules. In one case, possible changes in the location of objects are not visually presented, in the other case they are presented visually, which allows them to be correlated with the corresponding images.
Thus, the data obtained in both series of experiments with students of the second grade indicate that the use of two tasks to diagnose the formation of the cognitive metasubject competence associated with the ability to plan the solution of problems really makes it possible to take into account children with different degrees of formation of this competence.
In particular, in this case, it is possible to distinguish children with a greater formation of the ability to plan, children with a less formation of it, and children in whom this competence has not been formed.
At the same time, it is important that the tasks differ in the complexity of the problems
presented in them. In this case, this difference is manifested in the fact that the search for solutions in problems of different tasks ("Letters - numbers" and "Postman") is associated with the complexity of orientation in the conditions of the problems, which depends on the formal rules, which must be observed when solving problems.
This approach has certain advantages in diagnosing the cognitive competence in question. So, if diagnostics are carried out on the material of problems of only one task, then (if the problems are relatively difficult) it will be possible to distinguish only two groups of children. In one group there will be those who cope with the proposed problems, in the other - those who do not. Consequently, in the first group there will be those children for whom this competence has been formed, and in the second - for whom it has not been formed. With this approach, children who successfully cope only with simpler (than proposed) problems will not be taken into account.
If we carry out diagnostics on the material of one task, but built on the material of relatively simple problems, then it will also be possible to distinguish the same two groups of children: those who cope with, and those who do not cope with the proposed problems. But in this case, children who successfully cope with more complex (than proposed) problems, the solution of which is associated with the implementation of this competence, will no longer be taken into account.
So, the study showed the possibilities of a complex diagnostic method, on the basis of which three groups of children with different planning levels were identified. This method really made it possible to provide a more complete and more accurate diagnosis of the studied cognitive competence in second graders.
In the future, it is planned to conduct a number of studies with children of different ages in order, on the one hand, to identify students who have mastered planning at different levels, and on the other hand, to clarify the characteristics of this complex method.
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КОМПЛЕКСНЫЙ МЕТОД ДИАГНОСТИКИ ПЛАНИРОВАНИЯ В НАЧАЛЬНОЙ
ШКОЛЕ
А.З. Зак, вед. науч. сотр.
Психологический институт Российской академии образования (Россия, г. Москва)
Аннотация. В исследовании разработан комплекс из двух заданий, предназначенных для определения сформированности когнитивной метапредметной компетенции, связанной с умением планировать у младших школьников, в частности, у второклассников. Задачи первого задания создают более сложные условия для планирования решения, чем задачи второго задания. Такой подход позволяет выделить в учебном классе не две, как обычно, группы детей по сформированности познавательных действий, а три группы. Первую группу составляют дети решившие задачи обоих заданий, вторую группу - дети, решившие задачи только второго задания, третью группу - дети, не решившие задач обоих заданий. Апробация комплекса показала его эффективность для проведения более полной, чем обычно, диагностики умения планировать решение задач в начальных классах.
Ключевые слова: умение планировать, второклассники, комплекс из двух заданий, задание «Буквы, цифры», задание «Почтальон».
